import ECTate.Algebra.EllipticCurve.Kronecker import ECTate.Algebra.EllipticCurve.Model import ECTate.Algebra.ValuedRing import ECTate.Data.Nat.Enat import Mathlib.Data.Int.Basic import Mathlib.Tactic.LibrarySearch import Mathlib.Tactic.NormNum import Mathlib.Tactic.Contrapose open Enat variable {R :R: Type uType u} [Type u: Type (u + 1)inst :inst: IntegralDomain RIntegralDomainIntegralDomain: Type ?u.19993 → Type ?u.19993R] namespace Model variable {R: Type up :p: RR} defR: Type uis_local_singular_point (is_local_singular_point: {R : Type u} → [inst : IntegralDomain R] → {p : R} → SurjVal p → Model R → R × R → Propvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.21} → R → [inst : IntegralDomain R] → Type ?u.21p) (p: Re :e: Model RModelModel: (R : Type ?u.30) → [inst : IntegralDomain R] → Type ?u.30R) (R: Type uP :P: R × RR ×R: Type uR) :R: Type uProp :=Prop: Typevalp.valp: SurjVal pv (v: {R : Type ?u.43} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞weierstrassweierstrass: {R : Type ?u.50} → [inst : IntegralDomain R] → Model R → R × R → Ree: Model RP) >P: R × R0 ∧0: ?m.58valp.valp: SurjVal pv (v: {R : Type ?u.312} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞dweierstrass_dxdweierstrass_dx: {R : Type ?u.316} → [inst : IntegralDomain R] → Model R → R × R → Ree: Model RP) >P: R × R0 ∧0: ?m.320valp.valp: SurjVal pv (v: {R : Type ?u.338} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞dweierstrass_dydweierstrass_dy: {R : Type ?u.342} → [inst : IntegralDomain R] → Model R → R × R → Ree: Model RP) >P: R × R0 lemma (0: ?m.346valp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.383} → R → [inst : IntegralDomain R] → Type ?u.383p) (p: Re :e: Model RModelModel: (R : Type ?u.392) → [inst : IntegralDomain R] → Type ?u.392R) (h :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.397} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rdiscr >discr: {R : Type ?u.404} → [inst : IntegralDomain R] → Model R → R0) : ∃0: ?m.413P,P: ?m.671is_local_singular_pointis_local_singular_point: {R : Type ?u.673} → [inst : IntegralDomain R] → {p : R} → SurjVal p → Model R → R × R → Propvalpvalp: SurjVal pee: Model RP :=P: ?m.671∃ P, is_local_singular_point valp e PdefGoals accomplished! 🐙move_singular_point_to_origin_triple (move_singular_point_to_origin_triple: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → R × R × Revr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.707} → R → [inst : IntegralDomain R] → Type ?u.707p) (p: Re :e: Model RModelModel: (R : Type ?u.716) → [inst : IntegralDomain R] → Type ?u.716R) :R: Type uR ×R: Type uR ×R: Type uR := matchR: Type uevr.evr: EnatValRing presidue_char with |residue_char: {R : Type ?u.734} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → ℕ2 => (2: ℕevr.evr: EnatValRing pnorm_reprnorm_repr: {R : Type ?u.758} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Re.e: Model Ra4,a4: {R : Type ?u.762} → [inst : IntegralDomain R] → Model R → R0,0: ?m.772evr.evr: EnatValRing pnorm_repr (norm_repr: {R : Type ?u.835} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Re.e: Model Ra6 +a6: {R : Type ?u.842} → [inst : IntegralDomain R] → Model R → Re.e: Model Ra4 *a4: {R : Type ?u.848} → [inst : IntegralDomain R] → Model R → Re.e: Model Ra2)) |a2: {R : Type ?u.851} → [inst : IntegralDomain R] → Model R → R3 => (3: ℕevr.evr: EnatValRing pnorm_repr (-norm_repr: {R : Type ?u.1074} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Re.e: Model Rb6),b6: {R : Type ?u.1079} → [inst : IntegralDomain R] → Model R → R0,0: ?m.1118evr.evr: EnatValRing pnorm_repr (norm_repr: {R : Type ?u.1120} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Re.e: Model Ra3 -a3: {R : Type ?u.1127} → [inst : IntegralDomain R] → Model R → Re.e: Model Rb6 *b6: {R : Type ?u.1133} → [inst : IntegralDomain R] → Model R → Re.e: Model Ra1)) | _ => (a1: {R : Type ?u.1139} → [inst : IntegralDomain R] → Model R → R0,0: ?m.12790,0: ?m.12860) --need to fill here def0: ?m.1289move_singular_point_to_origin_iso (move_singular_point_to_origin_iso: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.2056} → R → [inst : IntegralDomain R] → Type ?u.2056p) (p: Re :e: Model RModelModel: (R : Type ?u.2065) → [inst : IntegralDomain R] → Type ?u.2065R) :R: Type uModelModel: (R : Type ?u.2069) → [inst : IntegralDomain R] → Type ?u.2069R :=R: Type urst_triplerst_triple: {R : Type ?u.2074} → [inst : IntegralDomain R] → Model R → R × R × R → Model Re (e: Model Rmove_singular_point_to_origin_triplemove_singular_point_to_origin_triple: {R : Type ?u.2079} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → R × R × Revrevr: EnatValRing pe) lemma (e: Model Revr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.2166} → R → [inst : IntegralDomain R] → Type ?u.2166p) (p: Re :e: Model RModelModel: (R : Type ?u.2171) → [inst : IntegralDomain R] → Type ?u.2171R) : (∃R: Type uP,P: ?m.2179is_local_singular_pointis_local_singular_point: {R : Type ?u.2181} → [inst : IntegralDomain R] → {p : R} → SurjVal p → Model R → R × R → Propvalpvalp: ?m.2163ee: Model RP) →P: ?m.2179is_local_singular_pointis_local_singular_point: {R : Type ?u.2200} → [inst : IntegralDomain R] → {p : R} → SurjVal p → Model R → R × R → Propvalp (valp: ?m.2163move_singular_point_to_origin_isomove_singular_point_to_origin_iso: {R : Type ?u.2210} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe) (e: Model R0,0: ?m.22220) :=0: ?m.2286(∃ P, is_local_singular_point valp e P) → is_local_singular_point valp (move_singular_point_to_origin_iso evr e) (0, 0)defGoals accomplished! 🐙pi_scaling (pi_scaling: {R : Type u} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.2324} → R → [inst : IntegralDomain R] → Type ?u.2324p) (p: Re :e: Model RModelModel: (R : Type ?u.2333) → [inst : IntegralDomain R] → Type ?u.2333R) :R: Type uModelModel: (R : Type ?u.2337) → [inst : IntegralDomain R] → Type ?u.2337R := { a1 :=R: Type uevr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2347} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.2360} → [inst : IntegralDomain R] → Model R → R1, a2 :=1: ?m.2364evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2374} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra2a2: {R : Type ?u.2384} → [inst : IntegralDomain R] → Model R → R2, a3 :=2: ?m.2388evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2393} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.2403} → [inst : IntegralDomain R] → Model R → R3, a4 :=3: ?m.2407evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2412} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra4a4: {R : Type ?u.2422} → [inst : IntegralDomain R] → Model R → R4, a6 :=4: ?m.2426evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2431} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra6a6: {R : Type ?u.2441} → [inst : IntegralDomain R] → Model R → R6 } lemma6: ?m.2445pi_scaling_of_b2 (pi_scaling_of_b2: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a2 ≥ ofN 2 → EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.2530} → R → [inst : IntegralDomain R] → Type ?u.2530p) (p: Re :e: Model RModelModel: (R : Type ?u.2539) → [inst : IntegralDomain R] → Type ?u.2539R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.2544} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.2551} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.2558} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.2564evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.2582} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.2586} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.2590} → [inst : IntegralDomain R] → Model R → R2) :2: ?m.2594evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2604} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb2b2: {R : Type ?u.2614} → [inst : IntegralDomain R] → Model R → R2 =2: ?m.2621evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2629} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.2639} → [inst : IntegralDomain R] → Model R → R1 *1: ?m.2643evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2645} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.2655} → [inst : IntegralDomain R] → Model R → R1 +1: ?m.26594 *4: ?m.2665evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.2674} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra2a2: {R : Type ?u.2684} → [inst : IntegralDomain R] → Model R → R2 :=2: ?m.2688R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a1) 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) 1) 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) + EnatValRing.sub_val evr (4 * e.a2) 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) (1 + 1)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr (b2 e) 2 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2lemmaGoals accomplished! 🐙pi_scaling_of_b4 (pi_scaling_of_b4: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a4 ≥ ofN 4 → EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.3323} → R → [inst : IntegralDomain R] → Type ?u.3323p) (p: Re :e: Model RModelModel: (R : Type ?u.3332) → [inst : IntegralDomain R] → Type ?u.3332R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.3337} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.3344} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.3351} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.3357evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.3375} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.3379} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.3383} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.3387evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.3397} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.3401} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.3405} → [inst : IntegralDomain R] → Model R → R4) :4: ?m.3409evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.3419} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb4b4: {R : Type ?u.3429} → [inst : IntegralDomain R] → Model R → R4 =4: ?m.3436evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.3444} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.3454} → [inst : IntegralDomain R] → Model R → R1 *1: ?m.3458evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.3460} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.3470} → [inst : IntegralDomain R] → Model R → R3 +3: ?m.34742 *2: ?m.3480evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.3489} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra4a4: {R : Type ?u.3499} → [inst : IntegralDomain R] → Model R → R4 :=4: ?m.3503R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) + EnatValRing.sub_val evr (2 * e.a4) 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) (1 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr (b4 e) 4 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4lemmaGoals accomplished! 🐙pi_scaling_of_b6 (pi_scaling_of_b6: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a6 ≥ ofN 6 → EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.4140} → R → [inst : IntegralDomain R] → Type ?u.4140p) (p: Re :e: Model RModelModel: (R : Type ?u.4149) → [inst : IntegralDomain R] → Type ?u.4149R) (h3 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.4154} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.4161} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.4168} → [inst : IntegralDomain R] → Model R → R3) (h6 :3: ?m.4174evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.4191} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.4195} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.4199} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.4203evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.4213} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb6b6: {R : Type ?u.4223} → [inst : IntegralDomain R] → Model R → R6 =6: ?m.4230evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.4238} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.4248} → [inst : IntegralDomain R] → Model R → R3 *3: ?m.4252evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.4254} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.4264} → [inst : IntegralDomain R] → Model R → R3 +3: ?m.42684 *4: ?m.4274evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.4283} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra6a6: {R : Type ?u.4293} → [inst : IntegralDomain R] → Model R → R6 :=6: ?m.4297R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a3 3 * e.a3) 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a3 * e.a3) 3) 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3) (3 + 3) + EnatValRing.sub_val evr (4 * e.a6) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) (3 + 3)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6lemmaGoals accomplished! 🐙pi_scaling_of_b8 (pi_scaling_of_b8: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a2 ≥ ofN 2 → SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a4 ≥ ofN 4 → SurjVal.v evr.valtn e.a6 ≥ ofN 6 → EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.4932} → R → [inst : IntegralDomain R] → Type ?u.4932p) (p: Re :e: Model RModelModel: (R : Type ?u.4941) → [inst : IntegralDomain R] → Type ?u.4941R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.4946} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.4953} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.4960} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.4966evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.4984} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.4988} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.4992} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.4996evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.5006} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.5010} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.5014} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.5018evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.5028} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.5032} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.5036} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.5040evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.5050} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.5054} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.5058} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.5062evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5072} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb8b8: {R : Type ?u.5082} → [inst : IntegralDomain R] → Model R → R8 =8: ?m.5089evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5112} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.5122} → [inst : IntegralDomain R] → Model R → R1 *1: ?m.5126evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5128} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.5138} → [inst : IntegralDomain R] → Model R → R1 *1: ?m.5142evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5144} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra6a6: {R : Type ?u.5154} → [inst : IntegralDomain R] → Model R → R6 -6: ?m.5158evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5166} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra1a1: {R : Type ?u.5176} → [inst : IntegralDomain R] → Model R → R1 *1: ?m.5180evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5182} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.5192} → [inst : IntegralDomain R] → Model R → R3 *3: ?m.5196evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5198} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra4a4: {R : Type ?u.5208} → [inst : IntegralDomain R] → Model R → R4 +4: ?m.52124 *4: ?m.5221evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5230} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra2a2: {R : Type ?u.5240} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.5244evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5246} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra6a6: {R : Type ?u.5256} → [inst : IntegralDomain R] → Model R → R6 +6: ?m.5260evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5268} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra2a2: {R : Type ?u.5278} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.5282evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5284} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.5294} → [inst : IntegralDomain R] → Model R → R3 *3: ?m.5298evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5300} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra3a3: {R : Type ?u.5310} → [inst : IntegralDomain R] → Model R → R3 -3: ?m.5314evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5319} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra4a4: {R : Type ?u.5329} → [inst : IntegralDomain R] → Model R → R4 *4: ?m.5333evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.5335} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Ra4a4: {R : Type ?u.5345} → [inst : IntegralDomain R] → Model R → R4 :=4: ?m.5349R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a1) 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) 1) 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1) (1 + 1) * e.a6) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1)) 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a1 1 * e.a3) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) 1) 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3) (1 + 3) * e.a4) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3)) 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2) 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2) 2 * e.a6) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (4 * e.a2 * e.a6) 2) 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * EnatValRing.sub_val evr e.a3 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) 3) 2 * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3) (3 + 2) * e.a3) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3)) 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr e.a4 4 * e.a4) 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (EnatValRing.sub_val evr (e.a4 * e.a4) 4) 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN 1 + ofN 1 + ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN 1 + ofN 1 + ofN 6
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN 1 + ofN 3 + ofN 4EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN 1 + ofN 1 + ofN 6
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN 1 + ofN 3 + ofN 4
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN 2 + ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN 1 + ofN 1 + ofN 6
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN 1 + ofN 3 + ofN 4
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN 2 + ofN 6
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN 2 + ofN 3 + ofN 3EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN 1 + ofN 1 + ofN 6
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN 1 + ofN 3 + ofN 4
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN 2 + ofN 6
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN 2 + ofN 3 + ofN 3
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN 4 + ofN 4EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (e.a1 * e.a3 * e.a4) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (e.a4 * e.a4) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + -EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + -EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) + EnatValRing.sub_val evr (-(e.a1 * e.a3 * e.a4)) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) + EnatValRing.sub_val evr (-(e.a4 * e.a4)) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6) (1 + 1 + 6) - EnatValRing.sub_val evr (e.a1 * e.a3 * e.a4) (1 + 3 + 4) + EnatValRing.sub_val evr (4 * e.a2 * e.a6) (2 + 6) + EnatValRing.sub_val evr (e.a2 * e.a3 * e.a3) (2 + 3 + 3) - EnatValRing.sub_val evr (e.a4 * e.a4) (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr (b8 e) 8 = EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
h116: SurjVal.v evr.valtn (e.a1 * e.a1 * e.a6) ≥ ofN (1 + 1 + 6)
h134: SurjVal.v evr.valtn (-(e.a1 * e.a3 * e.a4)) ≥ ofN (1 + 3 + 4)
h26: SurjVal.v evr.valtn (4 * e.a2 * e.a6) ≥ ofN (2 + 6)
h233: SurjVal.v evr.valtn (e.a2 * e.a3 * e.a3) ≥ ofN (2 + 3 + 3)
h44: SurjVal.v evr.valtn (-(e.a4 * e.a4)) ≥ ofN (4 + 4)open EnatValRing in lemmaGoals accomplished! 🐙pi_scaling_of_discr (pi_scaling_of_discr: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn (b2 e) ≥ ofN 2 → SurjVal.v evr.valtn (b4 e) ≥ ofN 4 → SurjVal.v evr.valtn (b6 e) ≥ ofN 6 → SurjVal.v evr.valtn (b8 e) ≥ ofN 8 → sub_val evr (discr e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.8108} → R → [inst : IntegralDomain R] → Type ?u.8108p) (p: Re :e: Model RModelModel: (R : Type ?u.8117) → [inst : IntegralDomain R] → Type ?u.8117R) (hb2 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.8122} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.8129} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb2 ≥ ofNb2: {R : Type ?u.8136} → [inst : IntegralDomain R] → Model R → R2) (hb4 :2: ?m.8145evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.8162} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.8166} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb4 ≥ ofNb4: {R : Type ?u.8170} → [inst : IntegralDomain R] → Model R → R4) (hb6 :4: ?m.8177evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.8187} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.8191} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb6 ≥ ofNb6: {R : Type ?u.8195} → [inst : IntegralDomain R] → Model R → R6) (hb8 :6: ?m.8202evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.8212} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.8216} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb8 ≥ ofNb8: {R : Type ?u.8220} → [inst : IntegralDomain R] → Model R → R8) :8: ?m.8227evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8237} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rdiscrdiscr: {R : Type ?u.8247} → [inst : IntegralDomain R] → Model R → R12 = -12: ?m.8254evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8275} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb2b2: {R : Type ?u.8285} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.8292evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8294} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb2b2: {R : Type ?u.8304} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.8311evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8313} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb8b8: {R : Type ?u.8323} → [inst : IntegralDomain R] → Model R → R8 -8: ?m.83308 * ((8: ?m.8336evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8348} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb4b4: {R : Type ?u.8358} → [inst : IntegralDomain R] → Model R → R4) ^4: ?m.83653) -3: ?m.836827 *27: ?m.8384evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8393} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb6b6: {R : Type ?u.8403} → [inst : IntegralDomain R] → Model R → R6 *6: ?m.8410evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8412} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb6b6: {R : Type ?u.8422} → [inst : IntegralDomain R] → Model R → R6 +6: ?m.84299 *9: ?m.8441evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8450} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb2b2: {R : Type ?u.8460} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.8467evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8469} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb4b4: {R : Type ?u.8479} → [inst : IntegralDomain R] → Model R → R4 *4: ?m.8486evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.8488} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb6b6: {R : Type ?u.8498} → [inst : IntegralDomain R] → Model R → R6 :=6: ?m.8505R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e * b2 e * b8 e) 12 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e * b2 e) 4 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e * b6 e) 12 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - sub_val evr (27 * b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e * b6 e) 12 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e * b4 e) 6 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + sub_val evr (9 * b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - sub_val evr (8 * b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e ^ 3) 12 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8sub_val evr (-b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8-sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6 = -sub_val evr (b2 e) 2 * sub_val evr (b2 e) 2 * sub_val evr (b8 e) 8 - 8 * sub_val evr (b4 e) 4 ^ 3 - 27 * sub_val evr (b6 e) 6 * sub_val evr (b6 e) 6 + 9 * sub_val evr (b2 e) 2 * sub_val evr (b4 e) 4 * sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbGoals accomplished! 🐙Goals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hx.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hxR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hyGoals accomplished! 🐙lemmaGoals accomplished! 🐙b2_of_pi_scaling (b2_of_pi_scaling: ∀ (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a2 ≥ ofN 2 → b2 (pi_scaling evr e) = EnatValRing.sub_val evr (b2 e) 2evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.12841} → R → [inst : IntegralDomain R] → Type ?u.12841p) (p: Re :e: Model RModelModel: (R : Type ?u.12850) → [inst : IntegralDomain R] → Type ?u.12850R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.12855} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.12862} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.12869} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.12875evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.12893} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.12897} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.12901} → [inst : IntegralDomain R] → Model R → R2) : (2: ?m.12905pi_scalingpi_scaling: {R : Type ?u.12915} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe).e: Model Rb2 =b2: {R : Type ?u.12922} → [inst : IntegralDomain R] → Model R → Revr.evr: EnatValRing psub_valsub_val: {R : Type ?u.12928} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb2b2: {R : Type ?u.12938} → [inst : IntegralDomain R] → Model R → R2 :=2: ?m.12945R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2b2 (pi_scaling evr e) = EnatValRing.sub_val evr (b2 e) 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 + 4 * EnatValRing.sub_val evr e.a2 2 = EnatValRing.sub_val evr (e.a1 * e.a1 + 4 * e.a2) 2R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2b2 (pi_scaling evr e) = EnatValRing.sub_val evr (b2 e) 2lemmaGoals accomplished! 🐙b4_of_pi_scaling (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.13210} → R → [inst : IntegralDomain R] → Type ?u.13210p) (p: Re :e: Model RModelModel: (R : Type ?u.13219) → [inst : IntegralDomain R] → Type ?u.13219R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13224} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13231} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.13238} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.13244evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13262} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13266} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.13270} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.13274evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13284} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13288} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.13292} → [inst : IntegralDomain R] → Model R → R4) : (4: ?m.13296pi_scalingpi_scaling: {R : Type ?u.13306} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe).e: Model Rb4 =b4: {R : Type ?u.13313} → [inst : IntegralDomain R] → Model R → Revr.evr: EnatValRing psub_valsub_val: {R : Type ?u.13319} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb4b4: {R : Type ?u.13329} → [inst : IntegralDomain R] → Model R → R4 :=4: ?m.13336R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4b4 (pi_scaling evr e) = EnatValRing.sub_val evr (b4 e) 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 + 2 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a3 + 2 * e.a4) 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4b4 (pi_scaling evr e) = EnatValRing.sub_val evr (b4 e) 4lemmaGoals accomplished! 🐙b6_of_pi_scaling (b6_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a6 ≥ ofN 6 → b6 (pi_scaling evr e) = EnatValRing.sub_val evr (b6 e) 6evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.13603} → R → [inst : IntegralDomain R] → Type ?u.13603p) (p: Re :e: Model RModelModel: (R : Type ?u.13612) → [inst : IntegralDomain R] → Type ?u.13612R) (h3 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13617} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13624} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.13631} → [inst : IntegralDomain R] → Model R → R3) (h6 :3: ?m.13637evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13654} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13658} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.13662} → [inst : IntegralDomain R] → Model R → R6) : (6: ?m.13666pi_scalingpi_scaling: {R : Type ?u.13676} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe).e: Model Rb6 =b6: {R : Type ?u.13683} → [inst : IntegralDomain R] → Model R → Revr.evr: EnatValRing psub_valsub_val: {R : Type ?u.13689} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb6b6: {R : Type ?u.13699} → [inst : IntegralDomain R] → Model R → R6 :=6: ?m.13706R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6b6 (pi_scaling evr e) = EnatValRing.sub_val evr (b6 e) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 + 4 * EnatValRing.sub_val evr e.a6 6 = EnatValRing.sub_val evr (e.a3 * e.a3 + 4 * e.a6) 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6b6 (pi_scaling evr e) = EnatValRing.sub_val evr (b6 e) 6lemmaGoals accomplished! 🐙b8_of_pi_scaling (b8_of_pi_scaling: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a2 ≥ ofN 2 → SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a4 ≥ ofN 4 → SurjVal.v evr.valtn e.a6 ≥ ofN 6 → b8 (pi_scaling evr e) = EnatValRing.sub_val evr (b8 e) 8evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.13971} → R → [inst : IntegralDomain R] → Type ?u.13971p) (p: Re :e: Model RModelModel: (R : Type ?u.13980) → [inst : IntegralDomain R] → Type ?u.13980R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.13985} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.13992} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.13999} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.14005evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14023} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14027} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.14031} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.14035evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14045} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14049} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.14053} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.14057evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14067} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14071} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.14075} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.14079evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14089} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14093} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.14097} → [inst : IntegralDomain R] → Model R → R6) : (6: ?m.14101pi_scalingpi_scaling: {R : Type ?u.14111} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe).e: Model Rb8 =b8: {R : Type ?u.14118} → [inst : IntegralDomain R] → Model R → Revr.evr: EnatValRing psub_valsub_val: {R : Type ?u.14124} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rb8b8: {R : Type ?u.14134} → [inst : IntegralDomain R] → Model R → R8 :=8: ?m.14141R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a6 6 - EnatValRing.sub_val evr e.a1 1 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a4 4 + 4 * EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a6 6 + EnatValRing.sub_val evr e.a2 2 * EnatValRing.sub_val evr e.a3 3 * EnatValRing.sub_val evr e.a3 3 - EnatValRing.sub_val evr e.a4 4 * EnatValRing.sub_val evr e.a4 4 = EnatValRing.sub_val evr (e.a1 * e.a1 * e.a6 - e.a1 * e.a3 * e.a4 + 4 * e.a2 * e.a6 + e.a2 * e.a3 * e.a3 - e.a4 * e.a4) 8lemmaGoals accomplished! 🐙val_b2_of_val_a12 (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.14447} → R → [inst : IntegralDomain R] → Type ?u.14447p) (p: Re :e: Model RModelModel: (R : Type ?u.14456) → [inst : IntegralDomain R] → Type ?u.14456R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14461} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14468} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.14475} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.14481evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14499} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14503} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.14507} → [inst : IntegralDomain R] → Model R → R2) :2: ?m.14511evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14521} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14525} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb2 ≥ ofNb2: {R : Type ?u.14529} → [inst : IntegralDomain R] → Model R → R2 :=2: ?m.14536R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙val_b4_of_val_a134 (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.14816} → R → [inst : IntegralDomain R] → Type ?u.14816p) (p: Re :e: Model RModelModel: (R : Type ?u.14825) → [inst : IntegralDomain R] → Type ?u.14825R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14830} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14837} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.14844} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.14850evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14868} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14872} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.14876} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.14880evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14890} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14894} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.14898} → [inst : IntegralDomain R] → Model R → R4) :4: ?m.14902evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.14912} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.14916} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb4 ≥ ofNb4: {R : Type ?u.14920} → [inst : IntegralDomain R] → Model R → R4 :=4: ?m.14927R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙val_b6_of_val_a36 (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.15216} → R → [inst : IntegralDomain R] → Type ?u.15216p) (p: Re :e: Model RModelModel: (R : Type ?u.15225) → [inst : IntegralDomain R] → Type ?u.15225R) (h3 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15230} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15237} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.15244} → [inst : IntegralDomain R] → Model R → R3) (h6 :3: ?m.15250evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15267} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15271} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.15275} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.15279evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15289} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15293} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb6 ≥ ofNb6: {R : Type ?u.15297} → [inst : IntegralDomain R] → Model R → R6 :=6: ?m.15304R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙val_b8_of_val_ai (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.15584} → R → [inst : IntegralDomain R] → Type ?u.15584p) (p: Re :e: Model RModelModel: (R : Type ?u.15593) → [inst : IntegralDomain R] → Type ?u.15593R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15598} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15605} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.15612} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.15618evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15636} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15640} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.15644} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.15648evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15658} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15662} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.15666} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.15670evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15680} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15684} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.15688} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.15692evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15702} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15706} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.15710} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.15714evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.15724} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.15728} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rb8 ≥ ofNb8: {R : Type ?u.15732} → [inst : IntegralDomain R] → Model R → R8 :=8: ?m.15739R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙discr_of_pi_scaling (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.16634} → R → [inst : IntegralDomain R] → Type ?u.16634p) (p: Re :e: Model RModelModel: (R : Type ?u.16643) → [inst : IntegralDomain R] → Type ?u.16643R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.16648} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.16655} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.16662} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.16668evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.16686} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.16690} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.16694} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.16698evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.16708} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.16712} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.16716} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.16720evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.16730} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.16734} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.16738} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.16742evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.16752} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.16756} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.16760} → [inst : IntegralDomain R] → Model R → R6) : (6: ?m.16764pi_scalingpi_scaling: {R : Type ?u.16774} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe).e: Model Rdiscr =discr: {R : Type ?u.16781} → [inst : IntegralDomain R] → Model R → Revr.evr: EnatValRing psub_valsub_val: {R : Type ?u.16787} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: Model Rdiscrdiscr: {R : Type ?u.16797} → [inst : IntegralDomain R] → Model R → R12 :=12: ?m.16804R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6discr (pi_scaling evr e) = EnatValRing.sub_val evr (discr e) 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6-EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b8 e) 8 - 8 * EnatValRing.sub_val evr (b4 e) 4 ^ 3 - 27 * EnatValRing.sub_val evr (b6 e) 6 * EnatValRing.sub_val evr (b6 e) 6 + 9 * EnatValRing.sub_val evr (b2 e) 2 * EnatValRing.sub_val evr (b4 e) 4 * EnatValRing.sub_val evr (b6 e) 6 = EnatValRing.sub_val evr (-b2 e * b2 e * b8 e - 8 * b4 e ^ 3 - 27 * b6 e * b6 e + 9 * b2 e * b4 e * b6 e) 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6discr (pi_scaling evr e) = EnatValRing.sub_val evr (discr e) 12lemmaGoals accomplished! 🐙val_discr_of_val_ai (val_discr_of_val_ai: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : Model R), SurjVal.v evr.valtn e.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.a2 ≥ ofN 2 → SurjVal.v evr.valtn e.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.a4 ≥ ofN 4 → SurjVal.v evr.valtn e.a6 ≥ ofN 6 → SurjVal.v evr.valtn (discr e) ≥ ofN 12evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.17281} → R → [inst : IntegralDomain R] → Type ?u.17281p) (p: Re :e: Model RModelModel: (R : Type ?u.17290) → [inst : IntegralDomain R] → Type ?u.17290R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17295} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17302} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra1 ≥ ofNa1: {R : Type ?u.17309} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.17315evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17333} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17337} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra2 ≥ ofNa2: {R : Type ?u.17341} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.17345evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17355} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17359} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra3 ≥ ofNa3: {R : Type ?u.17363} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.17367evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17377} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17381} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra4 ≥ ofNa4: {R : Type ?u.17385} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.17389evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17399} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17403} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Ra6 ≥ ofNa6: {R : Type ?u.17407} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.17411evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.17421} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.17425} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: Model Rdiscr ≥ ofNdiscr: {R : Type ?u.17429} → [inst : IntegralDomain R] → Model R → R12 :=12: ?m.17436R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
haR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: Model R
h1: SurjVal.v evr.valtn e.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.a6 ≥ ofN 6
hb2: SurjVal.v evr.valtn (b2 e) ≥ ofN 2
hb4: SurjVal.v evr.valtn (b4 e) ≥ ofN 4
hb6: SurjVal.v evr.valtn (b6 e) ≥ ofN 6
hb8: SurjVal.v evr.valtn (b8 e) ≥ ofN 8
hbend Model namespace ValidModel defGoals accomplished! 🐙pi_scaling (evr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.19032} → R → [inst : IntegralDomain R] → Type ?u.19032p) (p: ?m.19029e :e: ValidModel RValidModelValidModel: (R : Type ?u.19040) → [inst : IntegralDomain R] → Type ?u.19040R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.19049} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.19062} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.19077} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.19083evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.19101} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.19108} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 ≥ ofNa2: {R : Type ?u.19118} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.19122evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.19132} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.19136} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.19143} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.19147evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.19157} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.19161} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofNa4: {R : Type ?u.19168} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.19172evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.19182} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.19186} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofNa6: {R : Type ?u.19193} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.19197ValidModelValidModel: (R : Type ?u.19206) → [inst : IntegralDomain R] → Type ?u.19206R := { toModel :=R: Type uModel.pi_scalingModel.pi_scaling: {R : Type ?u.19220} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revrevr: EnatValRing pe.e: ValidModel RtoModel, discr_not_zero :=toModel: {R : Type ?u.19224} → [inst : IntegralDomain R] → ValidModel R → Model RR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6EnatValRing.sub_val evr (Model.discr e.toModel) 12 ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6EnatValRing.sub_val evr (Model.discr e.toModel) 12 ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': (let x := EnatValRing.sub_val evr (Model.discr e.toModel) 12; (fun x => p ^ 12 * x) x) = let x := 0; (fun x => p ^ 12 * x) xR: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': p ^ 12 * EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': Model.discr e.toModel = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': Model.discr e.toModel = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
H: EnatValRing.sub_val evr (Model.discr e.toModel) 12 = 0
H': Model.discr e.toModel = 0R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6Model.discr (Model.pi_scaling evr e.toModel) ≠ 0} lemmaGoals accomplished! 🐙toModel_pi_scaling (toModel_pi_scaling: ∀ {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6), (pi_scaling evr e h1 h2 h3 h4 h6).toModel = Model.pi_scaling evr e.toModelevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.20002} → R → [inst : IntegralDomain R] → Type ?u.20002p) (p: ?m.19999e :e: ValidModel RValidModelValidModel: (R : Type ?u.20010) → [inst : IntegralDomain R] → Type ?u.20010R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.20019} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.20032} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.20047} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.20053evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.20071} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.20078} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 ≥ ofNa2: {R : Type ?u.20088} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.20092evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.20102} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.20106} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.20113} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.20117evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.20127} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.20131} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofNa4: {R : Type ?u.20138} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.20142evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.20152} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.20156} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofNa6: {R : Type ?u.20163} → [inst : IntegralDomain R] → Model R → R6) : (6: ?m.20167e.e: ValidModel Rpi_scalingpi_scaling: {R : Type ?u.20177} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2 → SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4 → SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6 → ValidModel Revr h1 h2 h3 h4 h6).evr: EnatValRing ptoModel =toModel: {R : Type ?u.20198} → [inst : IntegralDomain R] → ValidModel R → Model Re.e: ValidModel RtoModel.toModel: {R : Type ?u.20201} → [inst : IntegralDomain R] → ValidModel R → Model Rpi_scalingpi_scaling: {R : Type ?u.20204} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → Model R → Model Revr :=evr: EnatValRing prfl defrfl: ∀ {α : Sort ?u.20226} {a : α}, a = aval_discr_to_nat {val_discr_to_nat: {R : Type u} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕp :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.20418} → R → [inst : IntegralDomain R] → Type ?u.20418p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.20427) → [inst : IntegralDomain R] → Type ?u.20427R) :R: Type uℕ :=ℕ: Typenat_of_valnat_of_val: {R : Type ?u.20435} → [inst : IntegralDomain R] → {p : R} → SurjVal p → {a : R} → a ≠ 0 → ℕvalpvalp: SurjVal pe.e: ValidModel Rdiscr_not_zero @[simp] lemmadiscr_not_zero: ∀ {R : Type ?u.20446} [inst : IntegralDomain R] (self : ValidModel R), Model.discr self.toModel ≠ 0iso_rst_val_discr_to_nat {iso_rst_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (r s t : R) (e : ValidModel R), val_discr_to_nat valp (rst_iso r s t e) = val_discr_to_nat valp ep :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.20507} → R → [inst : IntegralDomain R] → Type ?u.20507p) (p: Rrr: Rss: Rt :t: RR) (R: Type ue :e: ValidModel RValidModelValidModel: (R : Type ?u.20522) → [inst : IntegralDomain R] → Type ?u.20522R) :R: Type uval_discr_to_natval_discr_to_nat: {R : Type ?u.20527} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕvalp (valp: SurjVal prst_isorst_iso: {R : Type ?u.20537} → [inst : IntegralDomain R] → R → R → R → ValidModel R → ValidModel Rrr: Rss: Rtt: Re) =e: ValidModel Rval_discr_to_natval_discr_to_nat: {R : Type ?u.20542} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕvalpvalp: SurjVal pe :=e: ValidModel Rval_discr_to_nat valp (rst_iso r s t e) = val_discr_to_nat valp elemmaGoals accomplished! 🐙ofN_val_discr_to_nat {ofN_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (valp : SurjVal p) (e : ValidModel R), ofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.20944} → R → [inst : IntegralDomain R] → Type ?u.20944p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.20953) → [inst : IntegralDomain R] → Type ?u.20953R) : ofN (R: Type uval_discr_to_natval_discr_to_nat: {R : Type ?u.20958} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕvalpvalp: SurjVal pe) =e: ValidModel Rvalp.valp: SurjVal pvv: {R : Type ?u.20970} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rdiscr :=discr: {R : Type ?u.20977} → [inst : IntegralDomain R] → Model R → RofN (val_discr_to_nat valp e) = SurjVal.v valp (Model.discr e.toModel)R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
x✝: ℕ∪∞
h: SurjVal.v valp (Model.discr e.toModel) = x✝ofN (val_discr_to_nat valp e) = x✝R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (val_discr_to_nat valp e) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (val_discr_to_nat valp e) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (nat_of_val valp (_ : Model.discr e.toModel ≠ 0)) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (val_discr_to_nat valp e) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (val_discr_to_nat valp e) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNSurjVal.v valp (Model.discr e.toModel) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNSurjVal.v valp (Model.discr e.toModel) = ofN nR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
n: ℕ
h: SurjVal.v valp (Model.discr e.toModel) = ofN n
ofNofN (val_discr_to_nat valp e) = ofN nGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
x✝: ℕ∪∞
h: SurjVal.v valp (Model.discr e.toModel) = x✝ofN (val_discr_to_nat valp e) = x✝R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
h: SurjVal.v valp (Model.discr e.toModel) = ∞
topofN (val_discr_to_nat valp e) = ∞R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
h: SurjVal.v valp (Model.discr e.toModel) = ∞
top.hR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
h: SurjVal.v valp (Model.discr e.toModel) = ∞
topofN (val_discr_to_nat valp e) = ∞R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
h: SurjVal.v valp (Model.discr e.toModel) = ∞
top.h
top.h
top.h
top.hR: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
h: SurjVal.v valp (Model.discr e.toModel) = ∞
topofN (val_discr_to_nat valp e) = ∞lemmaGoals accomplished! 🐙pi_scaling_val_discr_to_nat {pi_scaling_val_discr_to_nat: ∀ {R : Type u} [inst : IntegralDomain R] {p : R} (evr : EnatValRing p) (e : ValidModel R) (h1 : SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1) (h2 : SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2) (h3 : SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3) (h4 : SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4) (h6 : SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6), val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12p :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.21227} → R → [inst : IntegralDomain R] → Type ?u.21227p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.21236) → [inst : IntegralDomain R] → Type ?u.21236R) (h1 :R: Type uevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.21241} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.21248} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.21260} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.21266evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.21284} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.21288} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 ≥ ofNa2: {R : Type ?u.21295} → [inst : IntegralDomain R] → Model R → R2) (h3 :2: ?m.21299evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.21309} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.21313} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.21320} → [inst : IntegralDomain R] → Model R → R3) (h4 :3: ?m.21324evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.21334} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.21338} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofNa4: {R : Type ?u.21345} → [inst : IntegralDomain R] → Model R → R4) (h6 :4: ?m.21349evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.21359} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.21363} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofNa6: {R : Type ?u.21370} → [inst : IntegralDomain R] → Model R → R6) :6: ?m.21374val_discr_to_natval_discr_to_nat: {R : Type ?u.21384} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕevr.evr: EnatValRing pvaltn (valtn: {R : Type ?u.21388} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal ppi_scalingpi_scaling: {R : Type ?u.21395} → [inst : IntegralDomain R] → {p : R} → (evr : EnatValRing p) → (e : ValidModel R) → SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1 → SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2 → SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3 → SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4 → SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6 → ValidModel Revrevr: EnatValRing pe h1 h2 h3 h4 h6) =e: ValidModel Rval_discr_to_natval_discr_to_nat: {R : Type ?u.21406} → [inst : IntegralDomain R] → {p : R} → SurjVal p → ValidModel R → ℕevr.evr: EnatValRing pvaltnvaltn: {R : Type ?u.21410} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pe -e: ValidModel R12 :=12: ?m.21418R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6ofN (val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6)) = ofN (val_discr_to_nat evr.valtn e - 12)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6SurjVal.v evr.valtn (Model.discr (pi_scaling evr e h1 h2 h3 h4 h6).toModel) = ofN (val_discr_to_nat evr.valtn e - 12)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6SurjVal.v evr.valtn (Model.discr (Model.pi_scaling evr e.toModel)) = ofN (val_discr_to_nat evr.valtn e - 12)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6SurjVal.v evr.valtn (EnatValRing.sub_val evr (Model.discr e.toModel) 12) = ofN (val_discr_to_nat evr.valtn e - 12)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
hSurjVal.v evr.valtn (Model.discr e.toModel) = ofN ?m.21563R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
hSurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6val_discr_to_nat evr.valtn (pi_scaling evr e h1 h2 h3 h4 h6) = val_discr_to_nat evr.valtn e - 12R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
hSurjVal.v evr.valtn (Model.discr e.toModel) = ofN (val_discr_to_nat evr.valtn e)R: Type u
inst: IntegralDomain R
p: R
evr: EnatValRing p
e: ValidModel R
h1: SurjVal.v evr.valtn e.toModel.a1 ≥ ofN 1
h2: SurjVal.v evr.valtn e.toModel.a2 ≥ ofN 2
h3: SurjVal.v evr.valtn e.toModel.a3 ≥ ofN 3
h4: SurjVal.v evr.valtn e.toModel.a4 ≥ ofN 4
h6: SurjVal.v evr.valtn e.toModel.a6 ≥ ofN 6
hSurjVal.v evr.valtn (Model.discr e.toModel) = SurjVal.v evr.valtn (Model.discr e.toModel)lemmaGoals accomplished! 🐙v_b2_of_v_a1_a2 {p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.21639} → R → [inst : IntegralDomain R] → Type ?u.21639p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.21648) → [inst : IntegralDomain R] → Type ?u.21648R) (h1 :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.21653} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.21665} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.21671valp.valp: SurjVal pvv: {R : Type ?u.21689} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 = ofNa2: {R : Type ?u.21696} → [inst : IntegralDomain R] → Model R → R1) :1: ?m.21700valp.valp: SurjVal pvv: {R : Type ?u.21706} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rb2 ≥ ofNb2: {R : Type ?u.21713} → [inst : IntegralDomain R] → Model R → R1 := val_add_ge_of_ge1: ?m.21720valp (val_mul_ge_of_left_gevalp: SurjVal pvalp h1) (val_mul_ge_of_right_gevalp: SurjVal pvalp (le_of_eq h2.symm)) lemmavalp: SurjVal pv_b4_of_v_a1_a3_a4 {p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.21890} → R → [inst : IntegralDomain R] → Type ?u.21890p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.21895) → [inst : IntegralDomain R] → Type ?u.21895R) (h1 :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.21900} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.21907} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.21911valp.valp: SurjVal pvv: {R : Type ?u.21918} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.21925} → [inst : IntegralDomain R] → Model R → Rq) (h4 :q: ?m.21885valp.valp: SurjVal pvv: {R : Type ?u.21933} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofN (a4: {R : Type ?u.21940} → [inst : IntegralDomain R] → Model R → Rq +q: ?m.218851)) :1: ?m.21947valp.valp: SurjVal pvv: {R : Type ?u.22004} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rb4 ≥ ofN (b4: {R : Type ?u.22011} → [inst : IntegralDomain R] → Model R → Rq +q: ?m.218851) :=1: ?m.22021R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙v_b6_of_v_a3_a6 {p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.22226} → R → [inst : IntegralDomain R] → Type ?u.22226p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.22231) → [inst : IntegralDomain R] → Type ?u.22231R) (h3 :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.22236} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.22243} → [inst : IntegralDomain R] → Model R → Rq) (h6 :q: ?m.22221valp.valp: SurjVal pvv: {R : Type ?u.22254} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofN (a6: {R : Type ?u.22261} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.22268q)) :q: ?m.22221valp.valp: SurjVal pvv: {R : Type ?u.22334} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rb6 ≥ ofN (b6: {R : Type ?u.22341} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.22351q) :=q: ?m.22221R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙v_b8_of_v_ai {v_b8_of_v_ai: ∀ {q : ℕ} {p : R} (valp : SurjVal p) (e : ValidModel R), SurjVal.v valp e.toModel.a1 ≥ ofN 1 → SurjVal.v valp e.toModel.a2 = ofN 1 → SurjVal.v valp e.toModel.a3 ≥ ofN q → SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1) → SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q) → SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.22648} → R → [inst : IntegralDomain R] → Type ?u.22648p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.22657) → [inst : IntegralDomain R] → Type ?u.22657R) (h1 :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.22741} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.22748} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.22752valp.valp: SurjVal pvv: {R : Type ?u.22759} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 = ofNa2: {R : Type ?u.22766} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.22770valp.valp: SurjVal pvv: {R : Type ?u.22776} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.22783} → [inst : IntegralDomain R] → Model R → Rq) (h4 :q: ?m.22726valp.valp: SurjVal pvv: {R : Type ?u.22791} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofN (a4: {R : Type ?u.22798} → [inst : IntegralDomain R] → Model R → Rq +q: ?m.227261)) (h6 :1: ?m.22805valp.valp: SurjVal pvv: {R : Type ?u.22862} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofN (a6: {R : Type ?u.22869} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.22876q)) :q: ?m.22726valp.valp: SurjVal pvv: {R : Type ?u.22938} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rb8 ≥ ofN (b8: {R : Type ?u.22945} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.22958q +q: ?m.227261) :=1: ?m.22968R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
hbGoals accomplished! 🐙lemmaGoals accomplished! 🐙v_discr_of_v_ai {v_discr_of_v_ai: ∀ {q : ℕ} {p : R} (valp : SurjVal p) (e : ValidModel R), q > 1 → SurjVal.v valp e.toModel.a1 ≥ ofN 1 → SurjVal.v valp e.toModel.a2 = ofN 1 → SurjVal.v valp e.toModel.a3 ≥ ofN q → SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1) → SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q) → SurjVal.v valp (Model.discr e.toModel) ≥ ofN (2 * q + 3)p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.24442} → R → [inst : IntegralDomain R] → Type ?u.24442p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.24431) → [inst : IntegralDomain R] → Type ?u.24431R) (R: Type uhq :hq: q > 1q >q: ?m.244371) (h1 :1: ?m.24453valp.valp: SurjVal pvv: {R : Type ?u.24490} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra1 ≥ ofNa1: {R : Type ?u.24502} → [inst : IntegralDomain R] → Model R → R1) (h2 :1: ?m.24508valp.valp: SurjVal pvv: {R : Type ?u.24526} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra2 = ofNa2: {R : Type ?u.24533} → [inst : IntegralDomain R] → Model R → R1) (h3 :1: ?m.24537valp.valp: SurjVal pvv: {R : Type ?u.24543} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra3 ≥ ofNa3: {R : Type ?u.24550} → [inst : IntegralDomain R] → Model R → Rq) (h4 :q: ?m.24437valp.valp: SurjVal pvv: {R : Type ?u.24558} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra4 ≥ ofN (a4: {R : Type ?u.24565} → [inst : IntegralDomain R] → Model R → Rq +q: ?m.244371)) (h6 :1: ?m.24572valp.valp: SurjVal pvv: {R : Type ?u.24629} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Ra6 ≥ ofN (a6: {R : Type ?u.24636} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.24643q)) :q: ?m.24437valp.valp: SurjVal pvv: {R : Type ?u.24705} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rdiscr ≥ ofN (discr: {R : Type ?u.24712} → [inst : IntegralDomain R] → Model R → R2 *2: ?m.24725q +q: ?m.244373) :=3: ?m.24735R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
haR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
ha.hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbGoals accomplished! 🐙R: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hbR: Type u
inst: IntegralDomain R
q: ℕ
p: R
valp: SurjVal p
e: ValidModel R
hq: q > 1
h1: SurjVal.v valp e.toModel.a1 ≥ ofN 1
h2: SurjVal.v valp e.toModel.a2 = ofN 1
h3: SurjVal.v valp e.toModel.a3 ≥ ofN q
h4: SurjVal.v valp e.toModel.a4 ≥ ofN (q + 1)
h6: SurjVal.v valp e.toModel.a6 ≥ ofN (2 * q)
h2': SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h4': SurjVal.v valp (Model.b4 e.toModel) ≥ ofN (q + 1)
h6': SurjVal.v valp (Model.b6 e.toModel) ≥ ofN (2 * q)
h8': SurjVal.v valp (Model.b8 e.toModel) ≥ ofN (2 * q + 1)
hblemma small_char_div_12 {Goals accomplished! 🐙p :p: RR} (hp :R: Type up =p: R2 ∨2: ?m.28044p =p: R3) (3: ?m.28122valp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.28176} → R → [inst : IntegralDomain R] → Type ?u.28176p) :p: Rvalp.valp: SurjVal pvv: {R : Type ?u.28184} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞12 ≥ ofN12: ?m.281921 :=1: ?m.28233Goals accomplished! 🐙Goals accomplished! 🐙Goals accomplished! 🐙lemmaGoals accomplished! 🐙v_rst_b2_of_small_char {p :p: RR} (R: Type uvalp :valp: SurjVal pSurjValSurjVal: {R : Type ?u.28902} → R → [inst : IntegralDomain R] → Type ?u.28902p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.28911) → [inst : IntegralDomain R] → Type ?u.28911R) (R: Type urr: Rss: Rt :t: RR) (h_b2 :R: Type uvalp.valp: SurjVal pvv: {R : Type ?u.28922} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞e.e: ValidModel Rb2 ≥ ofNb2: {R : Type ?u.28934} → [inst : IntegralDomain R] → Model R → R1) (h_p :1: ?m.28943valp.valp: SurjVal pvv: {R : Type ?u.28961} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞12 ≥ ofN12: ?m.289661) :1: ?m.29029valp.valp: SurjVal pv (v: {R : Type ?u.29036} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞rst_isorst_iso: {R : Type ?u.29040} → [inst : IntegralDomain R] → R → R → R → ValidModel R → ValidModel Rrr: Rss: Rtt: Re).e: ValidModel Rb2 ≥ ofNb2: {R : Type ?u.29046} → [inst : IntegralDomain R] → Model R → R1 :=1: ?m.29053R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
r, s, t: R
h_b2: SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h_p: SurjVal.v valp 12 ≥ ofN 1SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ≥ ofN 1R: Type u
inst: IntegralDomain R
p: R
valp: SurjVal p
e: ValidModel R
r, s, t: R
h_b2: SurjVal.v valp (Model.b2 e.toModel) ≥ ofN 1
h_p: SurjVal.v valp 12 ≥ ofN 1SurjVal.v valp (Model.b2 (Model.rst_iso r s t e.toModel)) ≥ ofN 1section cubic defGoals accomplished! 🐙Δcubic (c :Δcubic: {R : Type u} → [inst : IntegralDomain R] → R × R × R → RR ×R: Type uR ×R: Type uR) :R: Type uR :=R: Type u18 * c.18: ?m.292961 * c.1: {α : Type ?u.29306} → {β : Type ?u.29305} → α × β → α2.2: {α : Type ?u.29312} → {β : Type ?u.29311} → α × β → β1 * c.1: {α : Type ?u.29316} → {β : Type ?u.29315} → α × β → α2.2: {α : Type ?u.29320} → {β : Type ?u.29319} → α × β → β2 -2: {α : Type ?u.29324} → {β : Type ?u.29323} → α × β → β4 * c.4: ?m.293341 ^1: {α : Type ?u.29347} → {β : Type ?u.29346} → α × β → α3 * c.3: ?m.293512.2: {α : Type ?u.29361} → {β : Type ?u.29360} → α × β → β2 + c.2: {α : Type ?u.29365} → {β : Type ?u.29364} → α × β → β1 ^1: {α : Type ?u.29375} → {β : Type ?u.29374} → α × β → α2 * c.2: ?m.293792.2: {α : Type ?u.29392} → {β : Type ?u.29391} → α × β → β1 ^1: {α : Type ?u.29396} → {β : Type ?u.29395} → α × β → α2 -2: ?m.294004 * c.4: ?m.294132.2: {α : Type ?u.29426} → {β : Type ?u.29425} → α × β → β1 ^1: {α : Type ?u.29430} → {β : Type ?u.29429} → α × β → α3 -3: ?m.2943427 * c.27: ?m.294472.2: {α : Type ?u.29460} → {β : Type ?u.29459} → α × β → β2 ^2: {α : Type ?u.29464} → {β : Type ?u.29463} → α × β → β2 def2: ?m.29468model_to_cubic {model_to_cubic: {p : R} → EnatValRing p → ValidModel R → R × R × Rp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.32385} → R → [inst : IntegralDomain R] → Type ?u.32385p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.32394) → [inst : IntegralDomain R] → Type ?u.32394R) :R: Type uR ×R: Type uR ×R: Type uR := (R: Type uevr.evr: EnatValRing psub_valsub_val: {R : Type ?u.32412} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: ValidModel Ra2a2: {R : Type ?u.32430} → [inst : IntegralDomain R] → Model R → R1,1: ?m.32436evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.32450} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: ValidModel Ra4a4: {R : Type ?u.32463} → [inst : IntegralDomain R] → Model R → R2,2: ?m.32467evr.evr: EnatValRing psub_valsub_val: {R : Type ?u.32472} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → R → ℕ → Re.e: ValidModel Ra6a6: {R : Type ?u.32485} → [inst : IntegralDomain R] → Model R → R3) def3: ?m.32489cubic_has_dinstinct_roots {cubic_has_dinstinct_roots: {p : R} → EnatValRing p → ValidModel R → Propp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.32564} → R → [inst : IntegralDomain R] → Type ?u.32564p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.32573) → [inst : IntegralDomain R] → Type ?u.32573R) :R: Type uProp :=Prop: Typeevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.32582} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pv (v: {R : Type ?u.32589} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞Δcubic (Δcubic: {R : Type ?u.32596} → [inst : IntegralDomain R] → R × R × R → Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.32599} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pe)) =e: ValidModel R0 def δmultiplicity (c :0: ?m.32608R ×R: Type uR ×R: Type uR) :R: Type uR :=R: Type u3 * c.3: ?m.328882.2: {α : Type ?u.32898} → {β : Type ?u.32897} → α × β → β1 - c.1: {α : Type ?u.32904} → {β : Type ?u.32903} → α × β → α1 ^1: {α : Type ?u.32911} → {β : Type ?u.32910} → α × β → α2 def2: ?m.32915cubic_has_double_root {cubic_has_double_root: {p : R} → EnatValRing p → ValidModel R → Propp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.33482} → R → [inst : IntegralDomain R] → Type ?u.33482p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.33491) → [inst : IntegralDomain R] → Type ?u.33491R) :R: Type uProp :=Prop: Typeevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.33500} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pv (v: {R : Type ?u.33507} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞Δcubic (Δcubic: {R : Type ?u.33514} → [inst : IntegralDomain R] → R × R × R → Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.33517} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pe)) >e: ValidModel R0 ∧0: ?m.33526evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.33780} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pv (v: {R : Type ?u.33784} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞δmultiplicity (δmultiplicity: {R : Type ?u.33788} → [inst : IntegralDomain R] → R × R × R → Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.33791} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pe)) =e: ValidModel R0 def0: ?m.33796cubic_has_triple_root {cubic_has_triple_root: {p : R} → EnatValRing p → ValidModel R → Propp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.33830} → R → [inst : IntegralDomain R] → Type ?u.33830p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.33839) → [inst : IntegralDomain R] → Type ?u.33839R) :R: Type uProp :=Prop: Typeevr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.33848} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pv (v: {R : Type ?u.33855} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞Δcubic (Δcubic: {R : Type ?u.33862} → [inst : IntegralDomain R] → R × R × R → Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.33865} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pe)) >e: ValidModel R0 ∧0: ?m.33874evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.34128} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pv (v: {R : Type ?u.34132} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞δmultiplicity (δmultiplicity: {R : Type ?u.34136} → [inst : IntegralDomain R] → R × R × R → Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.34139} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pe)) >e: ValidModel R0 def0: ?m.34144move_cubic_double_root_to_origin_iso {move_cubic_double_root_to_origin_iso: {p : R} → EnatValRing p → ValidModel R → ValidModel Rp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.34179} → R → [inst : IntegralDomain R] → Type ?u.34179p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.34188) → [inst : IntegralDomain R] → Type ?u.34188R) :R: Type uValidModelValidModel: (R : Type ?u.34192) → [inst : IntegralDomain R] → Type ?u.34192R := let (R: Type ua2p,a2p: Ra4p2, ) :=a4p2: Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.34198} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pee: ValidModel Rrst_iso (rst_iso: {R : Type ?u.34255} → [inst : IntegralDomain R] → R → R → R → ValidModel R → ValidModel Rp * (p: Revr.evr: EnatValRing pnorm_repr (ifnorm_repr: {R : Type ?u.34261} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Revr.evr: EnatValRing presidue_char =residue_char: {R : Type ?u.34266} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → ℕ2 then2: ?m.34271a4p2 elsea4p2: Ra2p *a2p: Ra4p2)))a4p2: R00: ?m.3447400: ?m.34529e defe: ValidModel Rcubic_double_root_is_zero {cubic_double_root_is_zero: {p : R} → EnatValRing p → ValidModel R → Propp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.34865} → R → [inst : IntegralDomain R] → Type ?u.34865p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.34874) → [inst : IntegralDomain R] → Type ?u.34874R) :R: Type uProp := let (Prop: Typea2p,a2p: Ra4p2,a4p2: Ra6p3) :=a6p3: Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.34882} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pee: ValidModel Revr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.34939} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.34943} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a2p =a2p: R0 ∧0: ?m.34951evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.35201} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.35205} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a4p2 >a4p2: R0 ∧0: ?m.35210evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.35231} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.35235} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a6p3 >a6p3: R0 lemma {0: ?m.35240p :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.35366} → R → [inst : IntegralDomain R] → Type ?u.35366p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.35375) → [inst : IntegralDomain R] → Type ?u.35375R) :R: Type ucubic_has_double_rootcubic_has_double_root: {R : Type ?u.35380} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → Propevrevr: EnatValRing pe →e: ValidModel Rcubic_double_root_is_zerocubic_double_root_is_zero: {R : Type ?u.35393} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → Propevr (evr: EnatValRing pmove_cubic_double_root_to_origin_isomove_cubic_double_root_to_origin_iso: {R : Type ?u.35400} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → ValidModel Revrevr: EnatValRing pe) :=e: ValidModel Rsorry defsorry: ?m.35413move_cubic_triple_root_to_origin_iso {move_cubic_triple_root_to_origin_iso: {p : R} → EnatValRing p → ValidModel R → ValidModel Rp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.35435} → R → [inst : IntegralDomain R] → Type ?u.35435p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.35444) → [inst : IntegralDomain R] → Type ?u.35444R) :R: Type uValidModelValidModel: (R : Type ?u.35448) → [inst : IntegralDomain R] → Type ?u.35448R := let (R: Type ua2p, ,a2p: Ra6p3) :=a6p3: Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.35454} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pee: ValidModel Rrst_iso (rst_iso: {R : Type ?u.35511} → [inst : IntegralDomain R] → R → R → R → ValidModel R → ValidModel Rp * (p: Revr.evr: EnatValRing pnorm_repr (ifnorm_repr: {R : Type ?u.35517} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → R → Revr.evr: EnatValRing presidue_char =residue_char: {R : Type ?u.35522} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → ℕ2 then -2: ?m.35527a2p else -a2p: Ra6p3)))a6p3: R00: ?m.3570700: ?m.35762e defe: ValidModel Rcubic_triple_root_is_zero {cubic_triple_root_is_zero: {p : R} → EnatValRing p → ValidModel R → Propp :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.36076} → R → [inst : IntegralDomain R] → Type ?u.36076p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.36085) → [inst : IntegralDomain R] → Type ?u.36085R) :R: Type uProp := let (Prop: Typea2p,a2p: Ra4p2,a4p2: Ra6p3) :=a6p3: Rmodel_to_cubicmodel_to_cubic: {R : Type ?u.36093} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → R × R × Revrevr: EnatValRing pee: ValidModel Revr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.36150} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.36154} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a2p >a2p: R0 ∧0: ?m.36162evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.36416} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.36420} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a4p2 >a4p2: R0 ∧0: ?m.36425evr.evr: EnatValRing pvaltn.valtn: {R : Type ?u.36443} → {p : R} → [inst : IntegralDomain R] → EnatValRing p → SurjVal pvv: {R : Type ?u.36447} → {p : R} → [inst : IntegralDomain R] → SurjVal p → R → ℕ∪∞a6p3 >a6p3: R0 lemma {0: ?m.36452p :p: RR} (R: Type uevr :evr: EnatValRing pEnatValRingEnatValRing: {R : Type ?u.36578} → R → [inst : IntegralDomain R] → Type ?u.36578p) (p: Re :e: ValidModel RValidModelValidModel: (R : Type ?u.36587) → [inst : IntegralDomain R] → Type ?u.36587R) :R: Type ucubic_has_triple_rootcubic_has_triple_root: {R : Type ?u.36592} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → Propevrevr: EnatValRing pe →e: ValidModel Rcubic_triple_root_is_zerocubic_triple_root_is_zero: {R : Type ?u.36605} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → Propevr (evr: EnatValRing pmove_cubic_triple_root_to_origin_isomove_cubic_triple_root_to_origin_iso: {R : Type ?u.36612} → [inst : IntegralDomain R] → {p : R} → EnatValRing p → ValidModel R → ValidModel Revrevr: EnatValRing pe) :=e: ValidModel Rsorry end cubic end ValidModelsorry: ?m.36625